Quantum simulation of fermionic non-Abelian lattice gauge theories in $(2+1)$D with built-in gauge protection

• URL: http://arxiv.org/abs/2506.14747v1
• Date: Tue, 17 Jun 2025 17:37:40 GMT
• Title: Quantum simulation of fermionic non-Abelian lattice gauge theories in $(2+1)$D with built-in gauge protection
• Authors: Gaia De Paciani, Lukas Homeier, Jad C. Halimeh, Monika Aidelsburger, Fabian Grusdt,
• Abstract summary: Gauge-symmetry breaking is inevitable in established rishon-based schemes for alkaline-earth-like atoms (AELAs)<n>Here, we first construct a minimal model to quantum simulate non-Abelian LGTs ensuring that the gauge constraints are met and explicitly derive their unambiguous non-Abelian nature.<n>Second, we present a proposal for a novel gauge protection scheme using native interactions in AELAs enabling the simulation of toy models of non-Abelian $U(2)$ LGTs with dynamical fermionic matter in $(2+1)$ dimensions on large scales.
• Score: 0.0
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: Recent advancements in the field of quantum simulation have significantly expanded the potential for applications, particularly in the context of lattice gauge theories (LGTs). Maintaining gauge invariance throughout a simulation remains a central challenge, especially for large-scale non-Abelian LGTs with dynamical matter, which are particularly complex in terms of engineering for experiments. Gauge-symmetry breaking is inevitable in established rishon-based schemes for alkaline-earth-like atoms (AELAs) and controlling the magnitude of its effect is an open challenge. Here, we first construct a minimal model to quantum simulate non-Abelian LGTs ensuring that the gauge constraints are met and explicitly derive their unambiguous non-Abelian nature. Second, we present a proposal for a novel gauge protection scheme using native interactions in AELAs enabling the simulation of toy models of non-Abelian $U(2)$ LGTs with dynamical fermionic matter in $(2+1)$ dimensions on large scales. Due to the simplicity of the gauge protection mechanism, based on a Zeeman shift in combination with superexchange interactions, our scheme can be naturally included in other rishon-based quantum simulation protocols. Third, we extend our approach to a fully scalable, hybrid digital-analog simulator for $U(N)$ LGTs based on Rydberg AELA with variable rishon number. The proposed general mechanism for gauge protection provides a promising path towards the long-awaited simulation of non-Abelian LGTs relevant to particle physics.

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